Descriptive Statistics vs. Inferential Statistics. There are two types of statistical analysis: descriptive statistics and inferential statistics. Descriptive statistics refers to the methods employed in summarizing the obtained data into frequency distribution, percentage distribution, measures of central tendency, measures of position, measures of dispersion, measures of skewness, and kurtosis. Inferential statistics refers to the methods utilized in making and evaluating generalizations from obtained test scores. This includes interval estimation and hypothesis testing such as t-test, z-test, chi-square test, and analysis of variance (ANOVA).
Measures of Central Tendency. The measures of central tendency give concise information about the nature of the distribution of test scores. They serve as the representatives of the entire distribution of the set of test scores and present appropriate ways of how the scores tend toward the center.There are three commonly used measures of central tendency: the mean, the median, and the mode.
Lesson 3: Measures of Variability
a. The Range is the simplest and easiest measure. It simply measures how far the highest score is to the lowest score.
b. The Quartile Deviation (Q.D.) it is the average distance from the median to the two (2) quartiles, i.e., it tells how far the quartile points (Q1 and Q2) lie from the median, on the average.
c. The Standard Deviation (S.D.) it involves all scores in the distribution rather than through extreme scores. It may referred to as the root-mean-square of the deviation from the mean.
Lesson 4: Measures of Correlation
Educational data are not limited only to a set of test scores. There are instances wherein relationship between two sets of test scores (as between science and mathematics tests) has to be determined particularly in establishing a pattern as basis for predicting students’ performances.
The Coefficient of Correlation
The Correlation is measure of the strength of relationship and the direction of the relationship.
Interpreting Coefficient of Correlation
In interpreting the value of coefficient of correlation, the following table of categorization is used:
R(p) Descriptive Level
± 1.00 perfect correlation
Between ± 0.75 to ± 0.99 high correlation
Between ± 0.51 to ± 0.74 moderately high correlation
Between ± 0.31 to ± 0.50 moderately low correlation
between
±0.01 to ±0.30 low correlation
0.00 no correlation
THE SCATTER DIAGRAM
To have an idea of the degree of relationship between two sets of test scores, we make use of scatter plot. This technique consists of joining the points corresponding to the paired tests which are commonly represented by X and Y on the X-Y coordinate system.
PEARSON PRODUCT-MOMENT COEFFICIENT OF CORRELATION
The most commonly used measure of correlation. It is denoted by small letter (r).
where r= coefficient of correlation
X= the first set of test scores
Y= the second set of test scores
n= total number of pairing
SPEARMAN RANK-DIFFERENCE COEFFICIENT OF CORRELATION
There are instances, when the Pearson Product-Moment Coefficient of Correlation cannot be applied to a set of scores or even when it can be applied, some other methods may be more practical and more efficient to use. Spearman's rank-difference coefficient of correlation is applicable when the set is small. This technique may also be applied even if numerical values in the form of scores are available; ranks may be preferred.
Measures of Central Tendency. The measures of central tendency give concise information about the nature of the distribution of test scores. They serve as the representatives of the entire distribution of the set of test scores and present appropriate ways of how the scores tend toward the center.There are three commonly used measures of central tendency: the mean, the median, and the mode.
Lesson 3: Measures of Variability
a. The Range is the simplest and easiest measure. It simply measures how far the highest score is to the lowest score.
b. The Quartile Deviation (Q.D.) it is the average distance from the median to the two (2) quartiles, i.e., it tells how far the quartile points (Q1 and Q2) lie from the median, on the average.
c. The Standard Deviation (S.D.) it involves all scores in the distribution rather than through extreme scores. It may referred to as the root-mean-square of the deviation from the mean.
Lesson 4: Measures of Correlation
Educational data are not limited only to a set of test scores. There are instances wherein relationship between two sets of test scores (as between science and mathematics tests) has to be determined particularly in establishing a pattern as basis for predicting students’ performances.
The Coefficient of Correlation
The Correlation is measure of the strength of relationship and the direction of the relationship.
Interpreting Coefficient of Correlation
In interpreting the value of coefficient of correlation, the following table of categorization is used:
R(p) Descriptive Level
± 1.00 perfect correlation
Between ± 0.75 to ± 0.99 high correlation
Between ± 0.51 to ± 0.74 moderately high correlation
Between ± 0.31 to ± 0.50 moderately low correlation
between
±0.01 to ±0.30 low correlation
0.00 no correlation
THE SCATTER DIAGRAM
To have an idea of the degree of relationship between two sets of test scores, we make use of scatter plot. This technique consists of joining the points corresponding to the paired tests which are commonly represented by X and Y on the X-Y coordinate system.
PEARSON PRODUCT-MOMENT COEFFICIENT OF CORRELATION
The most commonly used measure of correlation. It is denoted by small letter (r).
where r= coefficient of correlation
X= the first set of test scores
Y= the second set of test scores
n= total number of pairing
SPEARMAN RANK-DIFFERENCE COEFFICIENT OF CORRELATION
There are instances, when the Pearson Product-Moment Coefficient of Correlation cannot be applied to a set of scores or even when it can be applied, some other methods may be more practical and more efficient to use. Spearman's rank-difference coefficient of correlation is applicable when the set is small. This technique may also be applied even if numerical values in the form of scores are available; ranks may be preferred.